If I bring a dead phone to a retail store, and it can't be fixed, how long will I have to wait?

If you mean an Apple Store, they replace iPhones, they do not repair them in the store. So unless the store happens to be out of stock of service replacements for your specific model, they'll replace it on the spot.

Regards.

Wait for what?

If it is defective then they will replace it on the spot.